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"contributors": [{"name": "Ida Friestad Pedersen", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/792/"}], "metadata": {"description": "", "licence": "None specified"}, "variables": {"a": {"description": "", "definition": "random(2..10 except 5)", "group": "Ungrouped variables", "templateType": "anything", "name": "a"}, "c": {"description": "", "definition": "random(-6..6 except b)", "group": "Ungrouped variables", "templateType": "anything", "name": "c"}, "d": {"description": "", "definition": "random(-10..10 except [b, c])", "group": "Ungrouped variables", "templateType": "anything", "name": "d"}, "b": {"description": "", "definition": "random(-6..6)", "group": "Ungrouped variables", "templateType": "anything", "name": "b"}, "n": {"description": "", "definition": "random(1..5)", "group": "Ungrouped variables", "templateType": "anything", "name": "n"}}, "advice": "", "ungrouped_variables": ["a", "n", "b", "c", "d"], "rulesets": {}, "preamble": {"css": "", "js": ""}, "tags": [], "variable_groups": [], "statement": "", "variablesTest": {"condition": "", "maxRuns": 100}, "parts": [{"type": "gapfill", "marks": 0, "gaps": [{"type": "jme", "marks": 1, "expectedVariableNames": [], "unitTests": [], "checkVariableNames": false, "variableReplacementStrategy": "originalfirst", "checkingType": "absdiff", "showCorrectAnswer": true, "showFeedbackIcon": true, "showPreview": true, "checkingAccuracy": 0.001, "customMarkingAlgorithm": "", "vsetRangePoints": 5, "answerSimplification": "all", "vsetRange": [0, 1], "failureRate": 1, "variableReplacements": [], "scripts": {}, "extendBaseMarkingAlgorithm": true, "answer": "{a}x+C"}, {"type": "jme", "marks": 1, "expectedVariableNames": [], "unitTests": [], "checkVariableNames": false, "variableReplacementStrategy": "originalfirst", "checkingType": "absdiff", "showCorrectAnswer": true, "showFeedbackIcon": true, "showPreview": true, "checkingAccuracy": 0.001, "customMarkingAlgorithm": "", "vsetRangePoints": 5, "answerSimplification": "all", "vsetRange": [0, 1], "failureRate": 1, "variableReplacements": [], "scripts": {}, "extendBaseMarkingAlgorithm": true, "answer": "{a+2}t+C"}], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "showFeedbackIcon": true, "steps": [{"type": "information", "marks": 0, "showCorrectAnswer": true, "unitTests": [], "variableReplacementStrategy": "originalfirst", "prompt": "<p>Du finner liknende eksempler i videosnutten&nbsp;Integrasjon av konstant funksjon:</p>\n<p><iframe width=\"480\" height=\"300\" frameborder=\"0\" src=\"https://www.educreations.com/lesson/embed/36560189/?ref=embed\" allowfullscreen=\"allowfullscreen\"></iframe></p>\n<p></p>", "showFeedbackIcon": true, "customMarkingAlgorithm": "", "variableReplacements": [], "scripts": {}, "extendBaseMarkingAlgorithm": true}], "prompt": "<p>Regn ut</p>\n<p>$\\displaystyle{\\int \\var{a} dx}$ =&nbsp;[[0]]</p>\n<p>$\\displaystyle{\\int \\var{a+2} dt}$ =&nbsp;[[1]]</p>", "customMarkingAlgorithm": "", "unitTests": [], "sortAnswers": false, "variableReplacements": [], "scripts": {}, "extendBaseMarkingAlgorithm": true, "stepsPenalty": 0}], "functions": {}, "type": "question"}, {"name": "Integrasjon 2", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Ida Friestad Pedersen", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/792/"}], "tags": [], "parts": [{"scripts": {}, "extendBaseMarkingAlgorithm": true, "stepsPenalty": 0, "type": "gapfill", "showCorrectAnswer": true, "prompt": "<p>Regn ut</p>\n<p>$\\displaystyle{\\int \\simplify{x^{n} }dx}$ =&nbsp;[[0]]</p>\n<p>$\\displaystyle{\\int \\simplify{t^{a}&nbsp;}dt}$ =&nbsp;[[1]]</p>", "marks": 0, "showFeedbackIcon": true, "variableReplacements": [], "steps": [{"scripts": {}, "extendBaseMarkingAlgorithm": true, "type": "information", "showCorrectAnswer": true, "prompt": "<p>Du finner noen liknende eksempler i videoen <a href=\"https://www.educreations.com/lesson/view/integrasjon-av-potenser/36560444/?s=zlVaJ7\">Integrasjon av potenser</a></p>\n<p><iframe width=\"480\" height=\"300\" frameborder=\"0\" src=\"https://www.educreations.com/lesson/embed/36560444/?s=zlVaJ7&amp;ref=embed\" allowfullscreen=\"allowfullscreen\"></iframe></p>", "marks": 0, "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "unitTests": [], "variableReplacements": [], "customMarkingAlgorithm": ""}], "sortAnswers": false, "variableReplacementStrategy": "originalfirst", "gaps": [{"scripts": {}, "extendBaseMarkingAlgorithm": true, "type": "jme", "showCorrectAnswer": true, "expectedVariableNames": [], "marks": 1, "showFeedbackIcon": true, "variableReplacements": [], "checkVariableNames": false, "checkingType": "absdiff", "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkingAccuracy": 0.001, "answerSimplification": "all", "variableReplacementStrategy": "originalfirst", "unitTests": [], "answer": "1/{n+1}x^{n+1}+C", "showPreview": true, "customMarkingAlgorithm": ""}, {"scripts": {}, "extendBaseMarkingAlgorithm": true, "type": "jme", "showCorrectAnswer": true, "expectedVariableNames": [], "marks": 1, "showFeedbackIcon": true, "variableReplacements": [], "checkVariableNames": false, "checkingType": "absdiff", "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkingAccuracy": 0.001, "answerSimplification": "all", "variableReplacementStrategy": "originalfirst", "unitTests": [], "answer": "1/{a+1}t^{a+1}+C", "showPreview": true, "customMarkingAlgorithm": ""}], "customMarkingAlgorithm": "", "unitTests": []}], "preamble": {"js": "", "css": ""}, "functions": {}, "advice": "", "metadata": {"description": "", "licence": "None specified"}, "variablesTest": {"maxRuns": 100, "condition": ""}, "statement": "", "rulesets": {}, "ungrouped_variables": ["a", "n", "b", "c", "d"], "variables": {"b": {"name": "b", "description": "", "templateType": "anything", "group": "Ungrouped variables", "definition": "random(-6..6)"}, "n": {"name": "n", "description": "", "templateType": "anything", "group": "Ungrouped variables", "definition": "random(1..5 except 4)"}, "c": {"name": "c", "description": "", "templateType": "anything", "group": "Ungrouped variables", "definition": "random(-6..6 except b)"}, "d": {"name": "d", "description": "", "templateType": "anything", "group": "Ungrouped variables", "definition": "random(-10..10 except [b, c])"}, "a": {"name": "a", "description": "", "templateType": "anything", "group": "Ungrouped variables", "definition": "random(1..10 except 2)"}}, "variable_groups": [], "type": "question"}, {"name": "Integrasjon 3", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Ida Friestad Pedersen", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/792/"}], "variablesTest": {"condition": "", "maxRuns": 100}, "tags": [], "variables": {"b": {"templateType": "anything", "description": "", "group": "Ungrouped variables", "definition": "random(-6..6)", "name": "b"}, "c": {"templateType": "anything", "description": "", "group": "Ungrouped variables", "definition": "random(-6..6 except b)", "name": "c"}, "d": {"templateType": "anything", "description": "", "group": "Ungrouped variables", "definition": "random(-10..10 except [b, c])", "name": "d"}, "n": {"templateType": "anything", "description": "", "group": "Ungrouped variables", "definition": "random(1..5)", "name": "n"}, "a": {"templateType": "anything", "description": "", "group": "Ungrouped variables", "definition": "random(2..10)", "name": "a"}}, "advice": "", "statement": "", "variable_groups": [], "metadata": {"description": "", "licence": "None specified"}, "functions": {}, "ungrouped_variables": ["a", "n", "b", "c", "d"], "preamble": {"js": "", "css": ""}, "parts": [{"showCorrectAnswer": true, "customMarkingAlgorithm": "", "marks": 0, "scripts": {}, "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "gaps": [{"showCorrectAnswer": true, "marks": 1, "answer": "{a}/4x^4+{b}/3x^3+{c}/2x^2+{d}x+C", "failureRate": 1, "variableReplacements": [], "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "checkingAccuracy": 0.001, "checkVariableNames": false, "vsetRangePoints": 5, "type": "jme", "answerSimplification": "all", "vsetRange": [0, 1], "expectedVariableNames": [], "showFeedbackIcon": true, "showPreview": true, "variableReplacementStrategy": "originalfirst", "unitTests": [], "checkingType": "absdiff"}], "steps": [{"showCorrectAnswer": true, "type": "information", "marks": 0, "customMarkingAlgorithm": "", "scripts": {}, "prompt": "<p>Du finner et liknende eksempel i videoen&nbsp;<a href=\"https://www.educreations.com/lesson/view/integrasjon-og-derivasjon/36562864/?s=x1Yimm\">Integrasjon og derivasjon</a></p>\n<p><iframe width=\"480\" height=\"300\" frameborder=\"0\" src=\"https://www.educreations.com/lesson/embed/36562864/?s=x1Yimm&amp;ref=embed\" allowfullscreen=\"allowfullscreen\"></iframe></p>", "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "unitTests": [], "extendBaseMarkingAlgorithm": true}], "type": "gapfill", "unitTests": [], "sortAnswers": false, "stepsPenalty": 0, "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "prompt": "<p>Regn ut</p>\n<p>$\\displaystyle{\\int \\left(\\simplify{{a}x^3+{b}x^2+{c}x+{d} }\\right)dx} =$&nbsp;[[0]]</p>"}], "rulesets": {}, "type": "question"}, {"name": "Integrasjon 4", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Ida Friestad Pedersen", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/792/"}], "variablesTest": {"condition": "", "maxRuns": 100}, "variables": {"c": {"description": "", "templateType": "anything", "definition": "random(-6..6 except [0, 2, a])", "name": "c", "group": "Ungrouped variables"}, "b": {"description": "", "templateType": "anything", "definition": "random(2..6)", "name": "b", "group": "Ungrouped variables"}, "m": {"description": "", "templateType": "anything", "definition": "random(2..4)", "name": "m", "group": "Ungrouped variables"}, "n": {"description": "", "templateType": "anything", "definition": "random(1..5 except 2)", "name": "n", "group": "Ungrouped variables"}, "a": {"description": "", "templateType": "anything", "definition": "random(2..10 except 3)", "name": "a", "group": "Ungrouped variables"}}, "tags": [], "advice": "", "statement": "", "variable_groups": [], "metadata": {"description": "", "licence": "None specified"}, "functions": {}, "ungrouped_variables": ["a", "b", "m", "n", "c"], "preamble": {"js": "", "css": ""}, "parts": [{"showCorrectAnswer": true, "customMarkingAlgorithm": "", "marks": 0, "scripts": {}, "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "gaps": [{"unitTests": [], "showCorrectAnswer": true, "checkVariableNames": false, "marks": 1, "variableReplacements": [], "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "checkingType": "absdiff", "vsetRange": [0, 1], "vsetRangePoints": 5, "type": "jme", "answerSimplification": "all, !Noleadingminus", "answer": "{a}/{n+1}x^{n+1}+{c}ln (abs(x))+C", "expectedVariableNames": [], "showFeedbackIcon": true, "showPreview": true, "variableReplacementStrategy": "originalfirst", "failureRate": 1, "checkingAccuracy": 0.001}], "steps": [{"showCorrectAnswer": true, "type": "information", "customMarkingAlgorithm": "", "marks": 0, "showFeedbackIcon": true, "extendBaseMarkingAlgorithm": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "prompt": "<p>Her bruker vi at&nbsp;</p>\n<p>$\\displaystyle{\\int \\frac{1}{x}dx =\\simplify{ln(abs(x))+C}}$</p>\n<p>Du finner et eksempel i videosnutten <a href=\"https://www.educreations.com/lesson/view/integrasjon-flerleddet-uttrykk-1/36561895/?s=axeYS2&amp;ref=link\">Integrasjon av uttrykk som inneholder 1/x</a>:</p>\n<p><iframe width=\"480\" height=\"300\" frameborder=\"0\" src=\"https://www.educreations.com/lesson/embed/36561895/?s=axeYS2&amp;ref=embed\" allowfullscreen=\"allowfullscreen\"></iframe></p>\n<p></p>", "unitTests": []}], "type": "gapfill", "prompt": "<p>Finn det ubestemte integralet</p>\n<p>$\\displaystyle{\\int \\left(\\simplify{{a}x^{n}+{c}/x}\\right)dx}$ =&nbsp;[[0]]</p>\n<p>NB: for &aring; skrive inn $\\simplify{abs(x)}$, kan du taste \"abs(x)\" (uten hermetegn)</p>", "sortAnswers": false, "stepsPenalty": 0, "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "unitTests": []}], "rulesets": {}, "type": "question"}, {"name": "Integrasjon av eksponentialfunksjoner 1", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Ida Friestad Pedersen", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/792/"}], "parts": [{"steps": [{"marks": 0, "variableReplacementStrategy": "originalfirst", "extendBaseMarkingAlgorithm": true, "type": "information", "variableReplacements": [], "customMarkingAlgorithm": "", "unitTests": [], "prompt": "<p>Du finner et lignende eksempel i videosnutten <a href=\"https://www.educreations.com/lesson/view/integrasjon-av-flerleddet-uttrykk-2/36562056/?s=7S2pBp&amp;ref=link\">Integrasjon av eksponentialfunksjoner</a></p>\n<p><iframe width=\"480\" height=\"300\" frameborder=\"0\" src=\"https://www.educreations.com/lesson/embed/36562056/?s=7S2pBp&amp;ref=embed\" allowfullscreen=\"allowfullscreen\"></iframe></p>", "scripts": {}, "showCorrectAnswer": true, "showFeedbackIcon": true}], "prompt": "<p>Regn ut det ubestemte integralet</p>\n<p>$\\displaystyle{\\int \\left(\\simplify{{a}exp({n}t)+{b}exp(-{m}t)}\\right)dt}=$ [[0]]</p>", "unitTests": [], "scripts": {}, "showCorrectAnswer": true, "showFeedbackIcon": true, "stepsPenalty": 0, "sortAnswers": false, "variableReplacementStrategy": "originalfirst", "type": "gapfill", "gaps": [{"showPreview": true, "answerSimplification": "all", "vsetRangePoints": 5, "checkingType": "absdiff", "unitTests": [], "scripts": {}, "showCorrectAnswer": true, "showFeedbackIcon": true, "answer": "{a}/{n}exp(({n}t))-{b}/{m}exp((-{m}t))+C", "marks": 1, "variableReplacementStrategy": "originalfirst", "expectedVariableNames": ["t"], "failureRate": 1, "checkingAccuracy": 0.001, "customMarkingAlgorithm": "", "type": "jme", "extendBaseMarkingAlgorithm": true, "vsetRange": [0, 1], "variableReplacements": [], "checkVariableNames": true}], "customMarkingAlgorithm": "", "marks": 0, "extendBaseMarkingAlgorithm": true, "variableReplacements": []}, {"steps": [{"marks": 0, "variableReplacementStrategy": "originalfirst", "extendBaseMarkingAlgorithm": true, "type": "information", "variableReplacements": [], "customMarkingAlgorithm": "", "unitTests": [], "prompt": "<p>Her kan vi starte med &aring; skrive om uttrykket:</p>\n<p>$\\displaystyle{\\int \\simplify{(e^({m+1}x)-{c})/e^({m+1}x)}dx= \\int \\left(\\simplify{e^({m+1}x)/e^({m+1}x)-{c}/e^({m+1}x)}\\right)dx = \\int \\left(\\simplify{1-{c}e^(-{m+1}x)}\\right)dx}$</p>\n<p>Deretter kan vi integrere ledd for ledd, p&aring; samme m&aring;te som i forrige oppgave.</p>", "scripts": {}, "showCorrectAnswer": true, "showFeedbackIcon": true}], "prompt": "<p>Regn ut det ubestemte integralet</p>\n<p>$\\displaystyle{\\int \\simplify{(e^({m+1}x)-{c})/e^({m+1}x)}dx}=$&nbsp;[[0]]</p>", "unitTests": [], "scripts": {}, "showCorrectAnswer": true, "showFeedbackIcon": true, "stepsPenalty": 0, "sortAnswers": false, "variableReplacementStrategy": "originalfirst", "type": "gapfill", "gaps": [{"showPreview": true, "answerSimplification": "all", "vsetRangePoints": 5, "checkingType": "absdiff", "unitTests": [], "scripts": {}, "showCorrectAnswer": true, "showFeedbackIcon": true, "answer": "x+{c}/{m+1}e^(-{m+1}x)+C", "marks": 1, "variableReplacementStrategy": "originalfirst", "expectedVariableNames": [], "failureRate": 1, "checkingAccuracy": 0.001, "customMarkingAlgorithm": "", "type": "jme", "extendBaseMarkingAlgorithm": true, "vsetRange": [0, 1], "variableReplacements": [], "checkVariableNames": false}], "customMarkingAlgorithm": "", "marks": 0, "extendBaseMarkingAlgorithm": true, "variableReplacements": []}], "variablesTest": {"maxRuns": 100, "condition": ""}, "variable_groups": [], "functions": {}, "advice": "", "rulesets": {}, "metadata": {"description": "", "licence": "None specified"}, "variables": {"c": {"name": "c", "description": "", "definition": "random(2..4)", "group": "Ungrouped variables", "templateType": "anything"}, "m": {"name": "m", "description": "", "definition": "random(1..4 except n)", "group": "Ungrouped variables", "templateType": "anything"}, "a": {"name": "a", "description": "", "definition": "random(1..4)", "group": "Ungrouped variables", "templateType": "anything"}, "b": {"name": "b", "description": "", "definition": "random(1..4 except a)", "group": "Ungrouped variables", "templateType": "anything"}, "n": {"name": "n", "description": "", "definition": "random(1..4 except a)", "group": "Ungrouped variables", "templateType": "anything"}}, "preamble": {"js": "", "css": ""}, "ungrouped_variables": ["a", "b", "c", "n", "m"], "tags": [], "statement": "", "type": "question"}, {"name": "Integrasjon av eksponentialfunksjoner 2", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Ida Friestad Pedersen", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/792/"}], "tags": [], "parts": [{"prompt": "<p>Finn det ubestemte integralet</p>\n<p>$\\displaystyle{\\int \\left(\\simplify{x^{n}+{b}^x}\\right)}dx =$&nbsp;[[0]]</p>", "extendBaseMarkingAlgorithm": true, "type": "gapfill", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "showFeedbackIcon": true, "variableReplacements": [], "steps": [{"prompt": "<p>Her kan vi bruke at $\\displaystyle{\\int a^x dx = \\frac{1}{\\ln a}a^x+C}$.</p>\n<p>Et lignende eksempel:</p>\n<p>$\\displaystyle{\\int (3x^2-10^x)dx = 3\\cdot \\frac{1}{3}x^3-\\frac{1}{\\ln 10}10^x+C = x^3 -\\frac{10^x}{\\ln 10} +C}$</p>", "extendBaseMarkingAlgorithm": true, "type": "information", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "customMarkingAlgorithm": "", "variableReplacements": [], "unitTests": []}], "sortAnswers": false, "variableReplacementStrategy": "originalfirst", "gaps": [{"scripts": {}, "extendBaseMarkingAlgorithm": true, "type": "jme", "showCorrectAnswer": true, "expectedVariableNames": [], "marks": 1, "showFeedbackIcon": true, "variableReplacements": [], "failureRate": 1, "checkingType": "absdiff", "checkVariableNames": false, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkingAccuracy": 0.001, "answer": "1/{n+1}x^{n+1}+1/ln({b})*{b}^x+C", "variableReplacementStrategy": "originalfirst", "answerSimplification": "all", "customMarkingAlgorithm": "", "showPreview": true, "unitTests": []}], "stepsPenalty": 0, "customMarkingAlgorithm": "", "unitTests": []}], "preamble": {"js": "", "css": ""}, "functions": {}, "advice": "", "metadata": {"description": "", "licence": "None specified"}, "variablesTest": {"maxRuns": 100, "condition": ""}, "statement": "", "rulesets": {}, "ungrouped_variables": ["n", "b"], "variables": {"b": {"name": "b", "description": "", "templateType": "anything", "group": "Ungrouped variables", "definition": "random(2..5 except [n, 10])"}, "n": {"name": "n", "description": "", "templateType": "anything", "group": "Ungrouped variables", "definition": "random(3..6)"}}, "variable_groups": [], "type": "question"}, {"name": "Integrasjon av trigonometriske funksjoner", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Ida Friestad Pedersen", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/792/"}], "variablesTest": {"condition": "", "maxRuns": 100}, "variables": {"b": {"description": "", "templateType": "anything", "group": "Ungrouped variables", "definition": "random(-5..5 except [0,a, -a])", "name": "b"}, "n": {"description": "", "templateType": "anything", "group": "Ungrouped variables", "definition": "random(2..6)", "name": "n"}, "a": {"description": "", "templateType": "anything", "group": "Ungrouped variables", "definition": "random(2..5)", "name": "a"}}, "tags": [], "advice": "", "statement": "", "variable_groups": [], "metadata": {"description": "", "licence": "None specified"}, "functions": {}, "ungrouped_variables": ["a", "b", "n"], "preamble": {"js": "", "css": ""}, "parts": [{"showCorrectAnswer": true, "customMarkingAlgorithm": "", "marks": 0, "scripts": {}, "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "gaps": [{"unitTests": [], "showCorrectAnswer": true, "customMarkingAlgorithm": "", "checkingType": "absdiff", "marks": 1, "checkingAccuracy": 0.001, "checkVariableNames": false, "scripts": {}, "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "vsetRange": [0, 1], "vsetRangePoints": 5, "type": "jme", "answerSimplification": "all, !Noleadingminus", "showPreview": true, "showFeedbackIcon": true, "answer": "-{a}cos(x)+{b}sin(x)+C", "variableReplacementStrategy": "originalfirst", "failureRate": 1, "expectedVariableNames": []}], "steps": [{"showCorrectAnswer": true, "type": "information", "customMarkingAlgorithm": "", "unitTests": [], "marks": 0, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "prompt": "<p>Husk at</p>\n<p>$\\displaystyle{\\int \\sin(x) dx = -\\cos(x)+C}$</p>\n<p>$\\displaystyle{\\int \\cos(x) dx = \\sin(x)+C}$</p>\n<p></p>", "variableReplacementStrategy": "originalfirst"}], "type": "gapfill", "unitTests": [], "sortAnswers": false, "stepsPenalty": 0, "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "prompt": "<p>Finn det ubestemte integralet</p>\n<p>$\\displaystyle{\\int \\left(\\simplify{{a}sin(x)+{b}cos(x)}\\right) dx}=$&nbsp;[[0]]</p>"}, {"showCorrectAnswer": true, "customMarkingAlgorithm": "", "marks": 0, "scripts": {}, "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "gaps": [{"unitTests": [], "showCorrectAnswer": true, "customMarkingAlgorithm": "", "checkingType": "absdiff", "marks": 1, "checkingAccuracy": 0.001, "checkVariableNames": false, "scripts": {}, "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "vsetRange": [0, 1], "vsetRangePoints": 5, "type": "jme", "answerSimplification": "all", "showPreview": true, "showFeedbackIcon": true, "answer": "{a*n}/pi sin(pi/{n}x-pi)+C", "variableReplacementStrategy": "originalfirst", "failureRate": 1, "expectedVariableNames": []}], "steps": [{"showCorrectAnswer": true, "type": "information", "customMarkingAlgorithm": "", "unitTests": [], "marks": 0, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "prompt": "<p>Du finner et lignende eksempel i videoen&nbsp;<a href=\"https://www.educreations.com/lesson/view/lineaer-kjerne-2/36577716/?s=6TiOyC&amp;ref=link\">Trigonometrisk funksjon med line&aelig;r kjerne</a></p>\n<p><iframe width=\"480\" height=\"300\" allowfullscreen=\"allowfullscreen\" src=\"https://www.educreations.com/lesson/embed/36577716/?s=6TiOyC&amp;ref=embed\" frameborder=\"0\"></iframe></p>", "variableReplacementStrategy": "originalfirst"}], "type": "gapfill", "unitTests": [], "sortAnswers": false, "stepsPenalty": 0, "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "prompt": "<p>Finn det ubestemte integralet</p>\n<p>$\\displaystyle{\\int \\simplify{{a}cos(pi/{n}x-pi)}dx}=$&nbsp;[[0]]</p>"}], "rulesets": {}, "type": "question"}, {"name": "Line\u00e6r nevner", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Ida Friestad Pedersen", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/792/"}], "metadata": {"description": "", "licence": "None specified"}, "variables": {"b": {"description": "", "definition": "random(-5..5 except [0,a, -a])", "group": "Ungrouped variables", "templateType": "anything", "name": "b"}, "a": {"description": "", "definition": "random(2..5)", "group": "Ungrouped variables", "templateType": "anything", "name": "a"}}, "advice": "", "ungrouped_variables": ["a", "b"], "rulesets": {}, "preamble": {"css": "", "js": ""}, "tags": [], "variable_groups": [], "statement": "", "variablesTest": {"condition": "", "maxRuns": 100}, "parts": [{"type": "gapfill", "showCorrectAnswer": true, "gaps": [{"type": "jme", "showCorrectAnswer": true, "expectedVariableNames": [], "unitTests": [], "checkVariableNames": false, "variableReplacementStrategy": "originalfirst", "checkingType": "absdiff", "marks": 1, "showFeedbackIcon": true, "showPreview": true, "checkingAccuracy": 0.001, "customMarkingAlgorithm": "", "vsetRangePoints": 5, "answerSimplification": "all, !Noleadingminus", "vsetRange": [0, 1], "failureRate": 1, "variableReplacements": [], "scripts": {}, "extendBaseMarkingAlgorithm": true, "answer": "1/{a}ln(abs({a}x+{b}))+C"}], "variableReplacementStrategy": "originalfirst", "marks": 0, "showFeedbackIcon": true, "steps": [{"type": "information", "showCorrectAnswer": true, "unitTests": [], "variableReplacementStrategy": "originalfirst", "marks": 0, "showFeedbackIcon": true, "extendBaseMarkingAlgorithm": true, "prompt": "<p>Du finner et lignende eksempel i videoen <a href=\"https://www.educreations.com/lesson/view/lineaer-kjerne-1/36577718/?s=LMhzmT&amp;ref=link\">Br&oslash;k med line&aelig;r nevner</a>:</p>\n<p><iframe width=\"480\" height=\"300\" allowfullscreen=\"allowfullscreen\" src=\"https://www.educreations.com/lesson/embed/36577718/?s=LMhzmT&amp;ref=embed\" frameborder=\"0\"></iframe></p>\n<p></p>\n<p></p>", "scripts": {}, "customMarkingAlgorithm": "", "variableReplacements": []}], "prompt": "<p>Finn det ubestemte integralet</p>\n<p>$\\displaystyle{\\int \\simplify{1/({a}x+{b})} dx}=$&nbsp;[[0]]</p>", "customMarkingAlgorithm": "", "unitTests": [], "sortAnswers": false, "variableReplacements": [], "scripts": {}, "extendBaseMarkingAlgorithm": true, "stepsPenalty": 0}], "functions": {}, "type": "question"}]}], "type": "exam", "contributors": [{"name": "Ida Friestad Pedersen", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/792/"}], "extensions": [], "custom_part_types": [], "resources": []}